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Boundary Smoothness conditions for functions in $R^p(X)$ (2108.02543v3)

Published 5 Aug 2021 in math.CV and math.FA

Abstract: Let $X$ be a compact subset of the complex plane and let $Rp(X)$, $2< p < \infty$, denote the closure of the rational functions with poles off $X$ in the $Lp$ norm. In this paper we consider three conditions that show how the functions in $Rp(X)$ can have a greater degree of smoothness at the boundary of $X$ than might otherwise be expected. We will show that two of the conditions are equivalent and imply the third but the third does not imply the other two.

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